extremal kragujevac trees with respect to randic energy

‎let $g$ be a simple graph with vertex set $v(g)={v_1‎, ‎v_2‎,‎dots,v_n}$‎. ‎the randi’c matrix of g‎, ‎represented as r(g)‎, ‎is‎ defined as the $n times n$ matrix whose $(i‎, ‎j)$-entry is‎ $(d_id_j)^{frac{-1}{2}}$‎ ‎if $v_i$ and $v_j$ are adjacent and 0 otherwise‎. ‎the randi’c energy of graph g is the sum of absolute values of the‎ ‎eigenvalues of r(g)‎. ‎in this study‎, ‎we determine the kragujevac trees with a fixed degree and fixed order that have maximal and minimal randić energy‎. additionally‎, ‎we obtain upper and lower bounds for the randić energy of these trees‎.